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Abstract

Operational risk losses are heavy tailed and are likely to be asymmetric and extremely
dependent among business lines/event types. The analysis of dependence via copula
models has been focussed on the bivariate case mainly. In the vast majority of
instances symmetric elliptical copulas are employed to model dependence for
severities.
This thesis proposes a new methodology to assess, in a multivariate way, the
asymmetry and extreme dependence between severities, and to calculate the capital
for operational risk. This methodology simultaneously uses (i) several parametric
distributions and an alternative mixture distribution (the Lognormal for the body of
losses and the generalised Pareto Distribution for the tail) using a technique from
extreme value theory, (ii) the multivariate skew t-copula applied for the first time
across severities and (iii) Bayesian theory. The former to model severities, I test
simultaneously several parametric distributions and the mixture distribution for each
business line. This procedure enables me to achieve multiple combinations of the
severity distribution and to find which fits most closely. The second to effectively
model asymmetry and extreme dependence in high dimensions. The third to estimate
the copula model, given the high multivariate component (i.e. eight business lines and
seven event types) and the incorporation of mixture distributions it is highly difficult
to implement maximum likelihood. Therefore, I use a Bayesian inference framework
and Markov chain Monte Carlo simulation to evaluate the posterior distribution to
estimate and make inferences of the parameters of the skew t-copula model.
The research analyses an updated operational loss data set, SAS® Operational
Risk Global Data (SAS OpRisk Global Data), to model operational risk at international
financial institutions. I then evaluate the impact of this multivariate, asymmetric and
extreme dependence on estimating the total regulatory capital, among other established
multivariate copulas. My empirical findings are consistent with other studies reporting
thin and medium-tailed loss distributions. My approach substantially outperforms
symmetric elliptical copulas, demonstrating that modelling dependence via the skew
t-copula provides a more efficient allocation of capital charges of up to 56% smaller
than that indicated by the standard Basel model.